In the previous installment, we discussed the use of a popular asset allocation/market timing rule (10M SMA rule hereafter) to size a short option position. The strategy did not work well as it was the case in traditional asset allocation. We thought that the poor performance was due to the fact that the 10M SMA rule is more of a market direction indicator that is not directly related to the PnL driver of a delta hedged position.

Recall that an option position can be loosely divided into 2 categories: dynamic and static [1]

1-Dynamic: the option position is delta hedged dynamically; its PnL driver is the implied/realized volatility dynamics. The profit and loss at the option expiration depends on the volatility dynamics, but not on the terminal value of the spot price.

2-Static: the option position is left unhedged; the payoff of the strategy depends on the spot price at option expiration but not on the volatility dynamics, i.e. it’s path independent.

In this post, we will apply the 10M SMA rule to a static, unhedged position. All other parameters and rules are the same as in our previous post. Briefly, the trading rules are as follows

1-NoTiming: Sell 1-Month at-the-money (ATM) put option, no rehedge.

2-10M-SMA: we only sell an ATM put option if the closing price of the underlying is greater than its 10M SMA.

Our rationale for investigating this case is that because the payoff of a static, unhedged position depends largely on the direction of the market, the 10M SMA timing rule will have a higher chance of success.

Table below summarizes and compares results of the short put strategy with and without the application of the 10M SMA rule

Strategy

NoTiming

10M-SMA

Number of Trades:

115

81

Percent Winners:

0.77

0.77

Average P&L:

65.69

62.77

Largest losing trade

-2702.50

-1601.00

Largest winning trade

652.00

451.50

Profit Factor (W/L):

1.47

1.54

Worst drawdown

-5002.50

-1897.00

Graph below shows the equity curves of the 2 strategies

As we can see from the Table and Graph, the 10M SMA rule performed better in this case. Although the win percentage and average PnL per trade remained approximately the same, the risks have been reduced significantly. The largest loss was reduced from $2.7K to $1.6K; drawdown decreased from $5K to $1.9K. As a result, the profit factor increased from 1.47 to 1.54.

In conclusion, the 10M SMA rule performs well in the case of a static, unhedged short put position. Using this rule, the risk-adjusted return of the trade was enhanced significantly.

Other related studies:

While researching the literature on this subject, I came across a similar study presented by E. Sinclair [2]. He showed that, for a delta hedged short strangle position, market timing based on the VIX index improved the results significantly. Since the VIX is a measure of volatility, its good performance is consistent with our understanding that for a delta hedged position, we should use a market timing indicator based on volatility and not on direction.

Last Wednesday, the SP500 index went down by just -1.8%, but in the volatility space it felt like the world was going to end; the volatility term structure, as measured by the VIX/VXV ratio, reached 1, i.e. the threshold where it passes from the contango to backwardation state. The near inversion of the volatility term structure can also be seen on the VIX futures curve (although to a lesser degree), as shown below.

VIX futures as at May 16 (blue line) and May 17 2017 (black line). Source: Vixcentral.com

With only -1.8% change in the underlying SPX, the associated spot VIX went from 10.65 to 15.59, a disproportional increase of 46%. The large changes in the spot and VIX futures were also reflected in the prices of VIX ETNs. For example, SVXY went down by about 18%, i.e. 9 times bigger than the SPX return. We note that in normal times SVXY has a beta of about 3-4 (as referenced to SPY).

So was the spike in volatility normal and what happened exactly?

To answer these questions, we first looked at the daily percentage changes of the VIX as a function of SPX returns. The Figure below plots the VIX changes v.s. SPX daily returns. Note that we plotted only days in which the underlying SPX decreased more than 1.5% from the previous day’s close. The arrow points to the data point of last Wednesday.

Daily VIX changes v.s. SPX returns

A cursory look at the graph can tell us that it’s rare that a small change in the underlying SPX caused a big percentage change in the VIX.

To quantify the probability, we counted the number of occurrences when the daily SPX returns are between -2.5% and -1.5%, but the VIX index experienced an increase of 30% or greater. The data set is from January 1990 to May 19 2017, and the total sample size is 6900.

There are only 11 occurrences, which means that volatility spikes like the one of last Wednesday occurred only about 0.16% of the time. So indeed, such an event is a rare occurrence.

Table below presents the dates and VIX changes on those 11 occurrences.

Date

VIX change

23/07/1990

0.515

03/08/1990

0.4068

19/08/1991

0.3235

04/02/1994

0.4186

30/05/2006

0.3086

27/04/2010

0.3057

25/02/2013

0.3402

15/04/2013

0.432

29/06/2015

0.3445

09/09/2016

0.3989

17/05/2017

0.4638

But what happened and what caused the VIX to go up that much?

While accurate answers must await thorough research, based on other results (not shown) and anecdotal evidences we believe that the rise in the popularity of VIX ETNs, and the resulting exponential increase in short interest, has contributed greatly to the increase in the volatility of volatility.

We also note that from the Table above, out of the 11 occurrences, more than half (6 to be precise) happened after 2010, i.e. after the introduction of VIX ETNs.

With an increase in volatility of volatility, risk management became more critical, especially if you are net short volatility and/or you have a lot of exposure to the skew (dGamma/dSpot).

Position sizing and portfolio allocation have not received much attention in the options trading community. In this post we are going to apply a simple position sizing rule and see how it performs within the context of volatility trading.

An option position can be sized by using, for example, a Markov Model where the size of the position can be a function of the regime transition probability [1]. While this is a research venue that we would like to explore, we decided to start with a simpler approach. We chose an algorithm that is intuitive enough for both quant and non-quant portfolio managers and traders.

We utilize the market timing rule proposed by Faber [2] who applied it to different asset classes in the context of portfolio allocation. The rule is as follows

Buy when monthly price > 10M SMA (10 Month Simple Moving Average)

Sell and move to cash when monthly price < 10M SMA

This remarkably simple timing rule has been used successfully by Faber and others. It has proved to significantly improve portfolios’ risk-adjusted returns [3].

Within the context of volatility trading, we compare 2 option strategies

1-NoTiming: Sell 1-Month at-the-money (ATM) put option on every option expiration Friday. The option is held until maturity, i.e. for a month. The position is kept delta neutral, i.e. it is rehedged at the end of every day.

2-10M-SMA: Similar to the above except that Faber’s timing rule is applied, i.e. we only sell an ATM put option if the closing price of the underlying is greater than its 10M SMA. Note, however, that unlike Faber, here we define the end of month as the option expiration Friday, and not the calendar end of month.

A short discussion on the rationale for choosing a market timing rule is in order here. Within the context of portfolio allocation, the 10M SMA rule is used for timing the direction of the market, i.e. the PnL driver is mostly market beta. Our trade’s PnL driver is, on the other hand, the dynamics of the implied/realized volatility spread. But as shown in a previous post, the IV/RV volatility dynamics correlates highly with the market returns. Therefore, we thought that we could use a directional timing strategy to size an options portfolio despite the fact that their PnL drivers are different, at least theoretically.

We tested the 2 strategies on SPY options from February 2007 to November 2016. Table below provides a summary of the trade statistics (average PnLs, winning/losing trades and drawdowns are in dollar).

Strategy

NoTiming

10M-SMA

Number of Trades

115

81

Percent Winners

0.68

0.69

Average P&L

18.84

14.87

Largest losing trade

-269.79

-248.50

Largest winning trade

243.54

154.22

Profit Factor (W/L)

1.77

1.64

Worst drawdown

-633.24

-339.91

Graph below shows the equity curves of the 2 strategies

As it is observed from the Table and the Graph, except for the worst drawdown, we don’t see much of an improvement when the 10M-SMA timing rule is applied. Although the 10M-SMA strategy avoided the worst period of the Global Financial Crisis, overall it made less money than the NoTiming strategy.

The non-improvement of Faber’s rule in the context of volatility selling probably relates to the fact that we are using a directional timing algorithm to size a trade whose PnL driver is the volatility dynamics . A position sizing algorithm based directly on the volatility dynamics would have a better chance of success. We are currently extending our research in this direction; any comment, feedback is welcome.

References:

[1] C. Donninger, Timing the Tail-Risk-Protection of the SPY with VIX-Futures by a Hidden Markov Model. The Wool-Milk-Sow Strategy. April 2017, http://www.godotfinance.com/pdf/TailRiskProtectionHMM.pdf

The spot VIX index finished last Friday at 11.28, a relatively low number, while the SKEW index was making a new high. The SKEW index is a good proxy for the cost of insurance and right now it appears to be expensive. A high reading of SKEW means investors are buying out of the money puts for protection.

CBOE SKEW index as at close of March 17, 2017. Source: Barchart.com

With the cost of insurance so high, is there a less expensive way for investors to hedge their portfolios?

One might think immediately of cross-asset hedging. However, if we use other underlying to hedge, we will then take on correlation (basis) risk and if not managed correctly, it can add risks to the portfolio instead of protecting it.

In this post we examine different hedging strategies using instruments on the same underlying. Our goal is to investigate the cost, risk/reward characteristics of each hedging strategy. Knowing the risk/reward profiles will allow us to design a cost-effective portfolio-protection scheme.

We will use Monte Carlo (MC) simulation to accomplish our goal [1]. The parameters and assumptions of the MC simulation are as follows:

Parameter

Value

Initial stock price

100

Volatility

20%

Risk-free rate

0.02

Drift

0.07

Days in simulation

252

Time step (day)

1

Number of paths

10000

Model

GBM [2]

The hedging strategies we’re investigating are:

1-NO HEDGE: no hedging is performed. The asset is allowed to evolve freely in a risky world. This would correspond to the portfolio of a Buy and Hold investor.

2-PPUT: protective put. We buy an at the money (ATM) put in order to hedge the downside. This strategy is the most common type of portfolio insurance.

3-GAMMA: convexity hedge. We buy an ATM put, but we then dynamically hedge it. This means that we flatten out the delta at the end of every day.

The GAMMA hedging strategy is not used frequently in the industry. The rationale for introducing it here is that given a high price of a put option, we will try to partially recoup its cost by actively scalping gamma, while we still benefit from the positive convexity of the option. This means that in case of a market correction, the gamma will manufacture negative delta so that the hedging position can offset some of the loss in the equity portfolio.

We use 10000 paths in our MC simulation. At the end of 1 year, we calculate the returns (using a Reg-T account) and determine its mean and variance. We also calculate the Value at Risk at 95% confidence interval. The graph below shows the histogram of the returns for the NO HEDGE strategy,

Return histogram for the NO HEDGE strategy

Table below presents the expected returns, standard deviations and Value at Risks for the hedging strategies.

Strategies

Expected return

Standard Deviation

Value at Risk

NO HEDGE

0.075

0.048

0.318

PPUT

0.052

0.024

0.118

GAMMA

0.066

0.029

0.248

As it is observed from the table, hedging with a protective put (PPUT) reduces the risks. Standard deviation and VaR are reduced from 0.048 and 0.318 to 0.024 to 0.118 respectively. However, the expected return is also reduced, from 0.075 to 0.052. This reduction is the cost of the insurance.

Interestingly, hedging using gamma convexity (GAMMA strategy) provides some reduction in risks (Standard deviation of 0.029, and VaR of 0.248), while not diminishing the returns greatly (expected return of 0.066).

In summary, GAMMA hedging is a strategy that is worth considering when designing a portfolio insurance scheme. It’s a good alternative to the often used protective (and expensive) put strategy.

Footnotes

[1] We note that the simulations were performed under idealistic assumptions, some are advantageous, and some are disadvantageous compared to a real life situation. However, results and the conclusion are consistent with our real world experience.

Last week the VIX index was more or less flat, the contango was favorable, and yet VIX ETF such as XIV, SVXY underperformed the market. In this post we will attempt to find an explanation.

As briefly mentioned in the footnotes of the blog post entitled “A Volatility Term Structure Based Trading Strategy”, VIX futures represent the (risk neutral) expectation values of the forward implied volatilities and not the spot VIX. The forward volatility is calculated as follows,

Using the above equation, and using the VIX index for σ0,t , VXV for σ0,T, we obtain the 1M-3M forward volatility as shown below.

1M-3M forward volatility from October 2016 to February 2017

Graph below shows the prices of VXX (green and red bars) and VIX April future (yellow line) for approximately the same period. Notice that their prices have increased since mid February, along with the forward volatility, while the spot VIX (not shown) has been more or less flat.

VXX (green and red bars) and VIX April future (yellow line) prices

If you define the basis as VIX futures price-spot VIX, then you will observe that last week this basis widened despite the fact that time to maturity shortened.

In summary, VIX futures and ETF traders should pay attention to forward volatilities, in addition to the spot VIX. Forward and spot volatilities often move together, but they diverge from time to time. The divergence is a source of risk as well as opportunity.

In previous blog posts, we explored the possibility of using various volatility indices in designing market timing systems for trading VIX-related ETFs. The system logic relies mostly on the persistent risk premia in the options market. Recall that there are 3 major types of risk premium:

1-Implied/realized volatilities (IV/RV)

2-Term structure

3-Skew

A summary of the systems developed based on the first 2 risk premia was published in this post.

In this article, we will attempt to build a trading system based on the third type of risk premium: volatility skew. As a measure of the volatility skew, we use the CBOE SKEW index.

According to the CBOE website, the SKEW index is calculated as follows,

The CBOE SKEW Index (“SKEW”) is an index derived from the price of S&P 500 tail risk. Similar to VIX®, the price of S&P 500 tail risk is calculated from the prices of S&P 500 out-of-the-money options. SKEW typically ranges from 100 to 150. A SKEW value of 100 means that the perceived distribution of S&P 500 log-returns is normal, and the probability of outlier returns is therefore negligible. As SKEW rises above 100, the left tail of the S&P 500 distribution acquires more weight, and the probabilities of outlier returns become more significant. One can estimate these probabilities from the value of SKEW. Since an increase in perceived tail risk increases the relative demand for low strike puts, increases in SKEW also correspond to an overall steepening of the curve of implied volatilities, familiar to option traders as the “skew”.

Our system’s rules are as follows:

Buy (or Cover) VXX if SKEW >= 10D average of SKEW

Sell (or Short) VXX if SKEW < 10D average of SKEW

The table below summarizes important statistics of the trading system

Initial capital

10000

Ending capital

40877.91

Net Profit

30877.91

Net Profit %

308.78%

Exposure %

99.50%

Net Risk Adjusted Return %

310.34%

Annual Return %

19.56%

Risk Adjusted Return %

19.66%

Max. system % drawdown

-76.00%

Number of trades

538

Winners

285 (52.97 %)

The graph below shows the equity line from February 2009 to December 2016

Portfolio equity for the volatility SKEW trading strategy

We observe that this system does not perform well as the other 2 systems [1]. A possible explanation for the weak performance is that VXX and other similar ETFs’ prices are affected more directly by the IV/RV relationship and the term structure than by the volatility skew. Hence using the volatility skew as a timing mechanism is not as accurate as other volatility indices.

In summary, the system based on the CBOE SKEW is not as robust as the VRP and RY systems. Therefore we will not add it to our existing portfolio of trading strategies.

Footnotes

[1] We also tested various combinations of this system and results lead to the same conclusion.

While the S&P 500 Index rose to an all-time high for a second day, the advance was accompanied by a gain in an options-derived gauge of trader stress that usually moves in the opposite direction

The article refers to a well-known phenomenon that under normal market conditions, the VIX and SP500 indices are negatively correlated, i.e. they tend to move in the opposite direction. However, when the market is nervous or in a panic mode, the VIX/SP500 relationship can break down, and the indices start to move out of whack.

In this post we revisit the relationship between the SP500 and VIX indices and attempt to quantify their dislocation. Knowing the SP500/VIX relationship and the frequency of dislocation will help options traders to better hedge their portfolios and ES/VX futures arbitrageurs to spot opportunities.

We first investigate the correlation between the SP500 daily returns and change in the VIX index [1]. The graph below depicts the daily changes in VIX as a function of SP500 daily returns from 1990 to 2016.

Daily point change in VIX v.s. SP500 return

We observe that there is a high degree of correlation between the daily SP500 returns and daily changes in the VIX. We calculated the correlation and it is -0.79 [2].

We next attempt to quantify the SP500/VIX dislocation. To do so, we calculated the residuals. The graph below shows the residuals from January to December 2016.

Residuals of VIX/SP500

Under normal market conditions, the residuals are small, reflecting the fact that SPX and VIX are highly (and negatively) correlated, and they often move in lockstep. However, under a market stress or nervous condition, SPX and VIX can get out of line and the residuals become large.

We counted the percentage of occurrences where the absolute values of the residuals exceed 1% and 2% respectively. Table below summarizes the results

Threshold

Percentage of Occurrences

1%

17.6%

2%

3.9%

We observe that the absolute values of SP500/VIX residuals exceed 1% about 17.6% of the time. This means that a delta-neutral options portfolio will experience a daily PnL fluctuation in the order of magnitude of 1 vega about 17% of the time, i.e. about 14 times per year. The dislocation occurs not infrequently.

The Table also shows that divergence greater than 2% occurs less frequently, about 3.8% of the time. This year, 2% dislocation happened during the January selloff, Brexit and the US presidential election.

Most of the time this kind of divergence is unpredictable. It can lead to a marked-to-market loss which can force the trader out of his position and realize the loss. So the key in managing an options portfolio is to construct positions such that if a divergence occurs, then the loss is limited and within the allowable limit.

Footnotes:

[1] We note that under different contexts, the percentage change in VIX can be used in a correlation study. In this post, however, we choose to use the change in the VIX as measured by daily point difference. We do so because the change in VIX can be related directly to Vega PnL of an options portfolio.

[2] The scope of this post is not to study the predictability of the linear regression model, but to estimate the frequency of SP500/VIX divergence. Therefore, we applied linear regression to the whole data set from 1990 to 2016. For more accurate hedges, traders should use shorter time periods with frequent recalibration.

Volatility trading strategies

In previous posts, we presented 2 volatility trading strategies: one strategy is based on the volatility risk premium (VRP) and the other on the volatility term structure, or roll yield (RY). In this post we present a detailed comparison of these 2 strategies and analyze their recent performance.

The first strategy (VRP) is based on the volatility risk premium. The trading rules are as follows [1]:

Buy (or Cover) VXX if VIX index <= 5D average of 10D HV of SP500

Sell (or Short) VXX if VIX index > 5D average of 10D HV of SP500

The second strategy (RY) is based on the contango/backwardation state of the volatility term structure. The trading rules are as follows:

Table below presents the backtested results from January 2009 to December 2016. The starting capital is $10000 and is fully invested in each trade (different position sizing scheme will yield different ending values for the portfolios. But the percentage return of each trade remains the same)

RY

VRP

Initial capital

10000

10000

Ending capital

179297.46

323309.02

Net Profit

169297.46

313309.02

Net Profit %

1692.97%

3133.09%

Exposure %

99.47%

99.19%

Net Risk Adjusted Return %

1702.07%

3158.54%

Annual Return %

44.22%

55.43%

Risk Adjusted Return %

44.46%

55.88%

Max. system % drawdown

-50.07%

-79.47%

Number of trades trades

32

55

Winners

15 (46.88 %)

38 (69.09 %)

We observe that RY produced less trades, has a lower annualized return, but less drawdown than VRP. The graph below depicts the portfolio equities for the 2 strategies.

Portfolio equity for the VRP and RY strategies

It is seen from the graph that VRP suffered a big loss during the selloff of Aug 2015, while RY performed much better. In the next section we will investigate the reasons behind the drawdown.

Performance during August 2015

The graph below depicts the 10-day HV of SP500 (blue solid line), its 5-day moving average (blue dashed line), the VIX index (red solid line) and its 5-day moving average (red dashed line) during July and August 2015. As we can see, an entry signal to go short was generated on July 21 (red arrow). The trade stayed short until an exit signal was triggered on Aug 31 (blue arrow). The system exited the trade with a large loss.

10-day Historical Volatility and VIX

The reason why the system stayed in the trade while SP500 was going down is that during that period, the VIX was always higher than 5D MA of 10D HV. This means that 10D HV was not a good approximate for the actual volatility during this highly volatile period. Recall that the expectation value of the future realized volatility is not observable. This drawdown provides a clear example that estimating actual volatility is not a trivial task.

By contrast, the RY strategy was more responsive to the change in market condition. It went long during the Aug selloff (blue arrow in the graph below) and exited the trade with a gain. The responsiveness is due to the fact that both VIX and VXV used to generate trading signals are observable. The graph below shows VIX/VXV ratio (black line) and its 5D moving average (red line).

VIX/VXV ratio

In summary, we prefer the RY strategy because of its responsiveness and lower drawdown. Both variables used in this strategy are observable. The VRP, despite being based on a good ground, suffers from a drawback that one of its variables is not observable. To improve it, one should come up with a better estimate for the expectation value of the future realized volatility. This task is, however, not trivial.

Last month was particularly favorable for short volatility strategies. In this post, we will investigate the reasons behind it.

First, the main PnL driver of a delta neutral, short gamma and short vega strategy is the spread between the implied volatility (IV) and the subsequently realized volatility (RV) of returns. Trading strategies such as long butterfly is profitable when, during the life of the position, RV is low compared to IV. The graph below shows the difference between IV and RV for SP500 during the last 5 months. (Note that RV is shifted by 1 month, so that IV-RV presents accurately the spread between the implied volatility and the volatility realized during the following month). As we can see from the graph, IV-RV was high, around 4%-7%, during October (the area around the “10/16” mark). Hence short volatility strategies were generally profitable during October.

IV-RV spreads of SP500

The second reason for the profitability is more subtle. The graph below shows the IV-RV spreads in function of monthly returns. As we can see, there is a high degree of correlation between IV-RV and the monthly returns. In fact, we calculated the correlation for the last 10 years and it is 0.69

IV-RV spreads v.s. SP500 monthly returns

This means that when IV-RV is high, SP500 usually trends up. This was the case, for example, during the month after Brexit (see the area around the “07/16” mark on the first graph). However, when the market trends, the cost of hedging in order to keep the position delta neutral is high. By contrast, even though IV-RV was high in October, the market moved in a range, thus helping us to minimize our hedging costs. This factor therefore contributed to the profitability of short volatility strategies.

In summary, October was favorable for short volatility strategies due to the high IV-RV spread and the range bound nature of the market.

In previous 2 articles, we explored a volatility trading strategy based on the volatility risk premium (VRP). The strategy performed well up until August 2015, and then it suffered a big loss during the August selloff.

In this article, we explore another volatility trading strategy, also discussed in Ref [1]. This strategy is based on the volatility term structure [2].

It is well known that volatilities exhibit a term structure which is similar to the yield curve in the interest rate market. The picture below depicts the volatility term structure for SP500 as at August 31 2016 [3].

SP500 Volatility Term Structure at Aug 31 2016

Most of the time the term structure is in contango. This means that the back months have higher implied volatilities than the front months. However, during a market stress, the volatility term structure curve usually inverts. In this case we say that the volatility term structure curve is in backwardation (a similar phenomenon exists in the interest rate market which is called inversion of the yield curve).

The basic idea of the trading strategy is to use the state (contango/backwardation) of the volatility term structure as a timing mechanism. Specifically, we go long if the volatility term structure is in backwardation and go short otherwise. To measure the slope of the term structure, we use the VIX and VXV volatility indices which represent the 1M and 3M implied volatilities of SP500 respectively.

[2] Note that there is a so-called term structure risk premium in the options market that is not often discussed in the literature. The strategy discussed in this post, however, is not meant to exploit the term structure risk premium. It uses the term structure as a timing mechanism.

[3] The volatility term structure presented here is calculated based on VIX futures, which are the expectation values of 30-day forward implied volatility. Therefore, it is theoretically different from the term structure of spot volatilities which are calculated from SP500 options. Practically speaking, the 2 volatility term structures are highly correlated, and we use the futures curve in this article for illustration purposes.